Exact 3D solution for static and damped harmonic response of simply supported general laminates

TL;DR

This paper develops exact three-dimensional solutions for static and damped harmonic responses of simply supported general laminates using an adapted state-space method, validated by finite element simulations and applicable to various laminate configurations.

Contribution

It introduces a general form of the state-space method capable of handling both static and dynamic behaviors of general laminates, including boundary condition considerations.

Findings

Validated solutions with finite element simulations.

Analyzed damped harmonic response of non-symmetrical sandwich laminates.

Studied static and dynamic behaviors of various laminate configurations.

Abstract

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [-15/15], [0/30/0] and [-10/0/40] laminates are studied for various length-to-thickness ratios.